Method of and apparatus for radiant energy measurement of impedance transitions in media, for identification and related purposes

ABSTRACT

This disclosure deals with measuring either discontinuous or continuous impedance transitions in various media to identify or delineate the properties and nature thereof by transmitting radiant energy waves to such media to produce reflected waves therefrom, deconvoluting the outgoing and returning waves, and integrating the resulting reflection impulse-response function so as to enable appropriate interpretation of the resulting display for identification and related purposes.

This is a divisional application of Ser. No. 494,907, filed Aug. 5, 1974now U.S. Pat. No. 4,094,304, which is a continuation of Ser. No.298,027, filed Oct. 16, 1972.

The present invention relates to methods of and apparatus for radiantenergy measurement of impedance transitions (continuous anddiscontinuous) in various media, for identification and relatedpurposes, being more particularly directed to the illumination of suchmedia by transmitting radiant energy thereto and reflecting the sametherefrom.

The radiant energy detection and navigation art is replete with systemsand techniques for making measurements for a myriad of purposes from thereflections or echoes of such energy transmitted to various media andobjects; electromagnetic radiant energy and acoustic radiant energybeing so used for continuous distance determination, for example, withthe latter being more particularly used for underwater or undergrounddetection, seismic prospecting and other purposes.

In accordance with the present invention, however, by using particulartypes of wave impulses and multiple receivers separated in the directionof transmission and reflection of the radiant energy waves, and throughappropriate deconvolution of outgoing and returning waves and subsequentintegration and appropriate display of the resulting reflectionimpulse-response function, entirely novel and different results areattained in that impedance transitions are interpretable, enabling notonly delineation of discrete layers of the media, but also quantitativegradual shifts in acoustic impedance therebetween that providediscrimination in determining the nature and properties thereof.

Such results are useful in a host of applications including, forexample, seismic prospecting, geological interpretation andidentification, determination of the nature of reflective media, and,more generally, indentification of the nature of otherwise unobservable,inaccessable, covered or otherwise hidden objects or other media,including, as further examples, reflective parts within human or animalbodies which have heretofore only been somewhat crudely outlined byacoustic reflection and related techniques.

For purposes of illustration, the invention will be hereinafterdescribed in detail in connection with the exemplary use of acousticradiant energy (and of preferred pulse types) useful for theillustrative examples of underwater seismic bottom-layer identification,the testing of laminates and the like, and the detection of reflectivesurfaces within human and animal bodies; though it is to be understood,as will be clear to those skilled in this art, that the novel methodhereinvolved is equally applicable to other applications, includingthose above-mentioned and those outlined in the hereinafter-describedprior patents and publications, and with other types of radiant energy,including electromagnetic waves, as well.

That acoustic impedance is a useful measure of normal sediment type,such that the measurement of specific acoustic impedance of an oceanbottom, for example, can be used to identify normal unconsolidatedmarine sediments, has previously been known, as described, for example,in the Bulletin of the Geological Society of America, Vol. 570, by E. L.Hamilton et al. Acoustic impedance can also be used to differentiateunconsolidated from consolidated sediments, or so-called basement rock.

It is also well known by those experienced in the art that the specificacoustic impedance of any sediment can be greatly reduced by thepresence of even small quantities of undissolved gas, such as areassociated with organic decay within sediments. Accordingly, the directquantitative measure of specific acoustic impedance, which is anobjective of the illustrative example herein of the seismic applicationof the method underlying this invention, can be of further utility inthe case of so-called "organic" sediments as a sensitive measure ofundissolved gas content, thereby allowing rapid, remote, indirectmeasure of decay, which can be a valuable index of gas-producingsediment pollutants.

The use of the before-mentioned deconvolution techniques, generally, isnot of itself new. Jens M. Hoven, for example, in a technical discussionentitled "Deconvolution for Removing the Effects of the Bubble Pulses ofExplosive Charges" published on page 281, Vol: 47, of the Journal of theAcoustical Society of America, disclosed that frequency-domaindeconvolution can be used for the quite different specific problem ofremoving redundant pulses associated with bubble pulse emissions. W. D.Moon et al in U.S. Pat. No. 3,489,996 also have employed similartechniques for removing surface-bottom multiples by deconvolution; andBennett, in U.S. Pat. No. 3,344,396 has disclosed that substantiallyupgoing signals can be deconvolved with substantially downgoing signalsto produce an amplitude-time signal which, in the terminology of linearcircuits, may be termed a reflection impulse-response function,before-mentioned. The reflection impulse-response function is to bepreferred because the process of deconvolution substantially improvesthe interpretability of the seismic waveforms by eliminating redundantand spurious events associated, for example, with multiple emissions bythe source or wave transmitter, and multiple surface and bottomreflections.

In accordance with the present invention, however, use is made ofimpedance properties and deconvolution techniques in a novel method andapparatus for attaining vastly improved results in identifying anddelineating the properties of media illuminated by radiant wave energy,such as the acoustic waves particularly applicable to underwater seismicapplications. Through the use of a preferred downgoing (incident)waveform and preferred sample timing, moreover, the results ofdeconvolution are substantially less sensitive to degradation as aresult of so-called noise. Additionally, it has been found that byintegrating the reflection impulse-response function, there results,unlike the prior art systems above-mentioned, a direct quantitativemeasure of specific acoustic impedance which, when appropriatelyinterpreted, can be used, in the illustrative example of seismicapplications, to identify sediments and/or to detect the presence andquantity of undissolved gas, such as is associated with organic decay.The relationships involved, furthermore, do not depend upon theexistence of discrete steps in specific acoustic impedance and are,therefore, unlike prior systems, suited to identification of gradualimpedance blends which are associated with transitions in sedimentarytype, or gradually varying gas content in "organic" or pollutedsediments.

A primary object of the invention, thus, is to provide a new andimproved method of and apparatus for acoustic radiant energy measurementof impedance transitions for identification and delineation of media,such as marine sediments in the case of underwater bottom applications,and for otherwise identifying and delineating the physical properties ofother media, in other applications.

A further object is to provide such a novel method and apparatus thatare adapted more generically for use with other types of radiant waveenergy, as well, including electromagnetic waves.

Still a further object is to provide a novel seismic prospectingapparatus and method.

A further object is to provide a new and improved method of an apparatusfor testing laminated and similar material layers.

An additional object is to provide a novel diagnostic method of andapparatus for identifying and delineating the properties and nature ofconcealed objects, including, but not limited to, objects within humanor animal bodies and the like.

Other and further objects will be explained hereinafter and are moreparticularly delineated in the appended claims. In summary, however, ina preferred mode, the invention contemplates, in connection with theillustrative seismic application, for example, the employment ofvirtually unipolar, preferably substantially time-asymmetric transmittedacoustic pulses, and, in some instances, at least a pair of receiverspositioned vertically, colinear with the transmitter source. Samplinginterval and instant, as well as receiver positions are preselected tosimplify calculation of upgoing and downgoing waves and greatly toreduce effects of additive noise. Upgoing and downgoing waves aredeconvolved, in the time domain, to produce a reflectionimpulse-response function which is integrated and displayed.Quantitative levels of the output display are related to sediment type,or gas content, even in the absence of discrete layers. Preferredtechniques and details, as well as applications to other than theseismic problems, are hereinafter presented.

The invention will now be described with reference to the accompanyingdrawing,

FIG. 1 of which is a schematic and block diagram illustrating apreferred embodiment employing the method of the invention;

FIGS. 2A, B and C are explanatory waveforms describing the performanceof the system of FIG. 1;

FIGS. 3B, 4B, 5A, and 5B are respectively diagrammatic views of displaysproduced by the invention and its correlation to bottom sediments, testresults and the like, with the results of FIGS. 3B and 4B applying,respectively, to the applications shown in FIGS. 3A and 4A; and

FIG. 6 is a similar view applied to reflections from within a skull of abody.

Prior to describing the embodiment of FIG. 1, it is in order to lay afoundation for the principles underlying the invention. From an analysisof errors resulting from so-called additive noise appearing in thereturning wave echo, reflection or upgoing waveform, resulting from,say, downward transmission of radiant energy from a source to thereflecting medium, it has been found that if the "noise" is zero mean,uncorrelated and stationary, then the variance of the p^(th) sample ofthe before-mentioned reflection impulse-response function issubstantially reduced if the following criteria are followed:

First, data is preferably sampled at substantially the Nyquist, orminimum sampling rate. Secondly, sampling instants are preferablyselected, or specifically prearranged (synchronized) so that the firstnontrivial downgoing or transmitted-wave sample is substantiallymaximum. Thirdly, a transmitter or source is selected which will, asmuch as possible, result in a small (substantially less than unity)error parameter E_(p), given substantially by the expression ##EQU1##where x_(s) is the s^(th) sample of the transmitted or downgoingwaveform and x_(n+1) is the first nontrivial downgoing wave sample.

It follows from the above that source-emitted pulse duration should notsignificantly exceed the reciprocal of the bandlimiting filter cut-offfrequency. In the preferred embodiment of FIG. 1, thus, the sourcewaveform, the filter cut-off frequency, the sampling rate and theinitial sampling instant are selected so as substantially to reduceerror in accordance with these criteria.

Referring to the application of FIG. 1, for example, the substantiallydowngoing transmitted and upgoing reflected waves must be used fordeconvolution to obtain the previously mentioned true reflectionimpulse-response function. If two receivers or detecting means arevertically displaced as illustrated and later described in more detail,then the vertically traveling downgoing and upgoing waves can beextracted from the two observed waveforms at the two receivers, providedthe acoustic travel time between the two receivers is known orobservable. The advantages of a vertically displaced pair of receiversover more conventional so-called directive receivers is that the pair ofreceivers will effectively separate low-frequency waves which are ofparticular utility in applications such as seismic prospecting and thelike. Sampling intervals are preselected readily to generate upgoing anddowngoing waves, as later explained.

It has been found, in accordance with the invention, that the reflectionimpulse-response function, R(2t), corresponding to reflection from aregion of modest continuous impedance change along the incident axis, isgiven by the expression R(2t)≈(dz/dt)/4z; and its integral is given bythe equation ##EQU2## where z(t) is the relationship between impedanceand acoustic travel time t, and z_(o) is the specific acoustic impedanceof the medium in which the receivers are located. In the preferredembodiment, the reflection impulse-response function is integrated toobtain the sediment or other medium acoustic impedance as a function oftravel time, using substantially the relationship ##EQU3## In theseismic application, specific acoustic impedance is used to determinesediment type or, alternatively, undissolved gas content, usingrelationships such as those of Hamilton (previously cited) and A. B.Wood in A Textbook of Sound, published by MacMillan Co. in 1955,describing a relationship between undissolved gas (air) content andacoustic velocity. Since bulk density is insignificantly affected bysmall volume percentages of undissolved gas, Wood's theory enables us torelate acoustic impedance (bulk density times longitudinal velocity) togas content.

The details of the system of FIG. 1 will now be described in connectionwith the illustrative example of seismic underwater operations, thoughits direct application to other uses will be evident and later morefully discussed. An impulsive wave-transmitting source is shown at 1supported by a framework 4 at its upper end, the base of which restsupon the medium 5 to be studied, such as bottom sediments or the like.Vertically positioned below the source 1 and supported by the frame 4are at least two substantially colinear receivers 2 and 3, in turnvertically separated in separate planes from one another in thedirection of downgoing radiant wave-energy transmission from the source1 to illuminate the medium 5, and of opposite-direction upgoingreflection, echoing or return therefrom.

A variable frequency square-wave generator 6 is shown provided with acapacitive coupling output circuit 7 for generating a series ofalternating polarity pulses, FIG. 2(A). Upon closure of anevent-initiation switch 8, short alternate polarity pulses are thusintroduced into both a trigger pulse former 9, via line 11, and theintensity (z-axis) modulation input of a dual beam cathode-rayoscilloscope or other display 10. The trigger pulse former, upon receiptof a positive-going pulse in the input line 11, generates a singleelectrical pulse in the output 12, which serves both to trigger thesource 1 through an energy storage power pack 13, and the triggeringsweep of the display 10. The medium 5 becomes thus illuminated by thedowngoing transmission from the source 1, and the upgoing reflectionsare received successively at the receivers 3 and 2, being filtered withrespective so-called low-pass variable cut-off filters 14 and 15 andapplied at Input₁ and Input₂ to the display at 10.

Upon each closure of the event-initiation switch 8, the received signalwaveforms from receivers 2 and 3, which are thus effective for receptionand display only during such sampling instants, are oscillographicallydisplayed, with timing events appearing, for example, as variations intrace intensity. In a preferred embodiment, the frequency of thesquare-wave generator 6 is adjusted after each event so as to bring theobserved waveforms into a preferred prealignment or synchronization, asshown and later described in connection with FIGS. 2B and C. In suchsynchronized condition, the periodic sampling interval shown at 16, FIG.2A, has been successively adjusted until the first wave-signal arrivalat the second receiver 3 is precisely n times the reference interval 16,where n is an integer (for example, n=5 in FIG. 2). For each sampledevent, the time reference 17 corresponds to triggering of the source 1,and is the instant of the first positive going pulse, FIG. 2A, afterclosure of the event-initiation switch 8. If the upper receiver 2 hasbeen properly positioned, the first wave-signal arrival will beprecisely m (integer) times the reference interval 16 (with m equalling,say, 3 in FIG. 2). To attain these relationships, small finaladjustments in the position of upper receiver 2 may be effected, ifnecessary, by an adjustable support arm 18. Once synchronization hasbeen so achieved, the bandlimiting filters 14 and 15 are tuned oradjusted to substantially the so-called Nyquist frequency correspondingto a sampling interval equal to the reference interval 16. The recordingor displaying switch 19 is then closed to enable digital recordingand/or display at 10 of the reflected waves received at receivers 2 and3 at simultaneous sample instants 17, 17', 17", 17'", etc. usingrespective transient recorders 20 and 21.

Designating successive sample values of the waveform from receiver 2 asP₀, P₁, P₂, P₃, etc. (as shown by sample points 22, 22', 22", 22'",22^(iv), etc. in FIG. 2B) and sampled values from receiver 3 as q₀, q₁,q₂, q₃, etc., (as indicated by points 23, 23', 23", 23'", etc. in FIG.2C), the following preferred, or substantially similar algorithms may beused numerically to compute the downgoing wave sample values x₀, x₁, x₂,. . . x_(s) . . . , and upgoing wave sample values y₀, y₁, y₂, . . .y_(s), as determined by the following expressions:

                  Table I                                                         ______________________________________                                         ##STR1##                                                                      ##STR2##     [q.sub.s - x.sub.s ]                                            P.sub.s 0    (s≦m); and                                                q.sub.s 0    (s≦n).                                                    ______________________________________                                    

Upgoing and downgoing waveforms y_(s) and x_(s) can be deconvolved byany of the so-called inverse filter techniques well known to thoseversed in the art as described, for example, in the before-citedpublications. In a preferred technique, upgoing and downgoing waves aretime-domain deconvolved, thereby avoiding errors associated with timetruncation of waveforms, with the resulting reflection impulse-responsefunction being integrated and the specific acoustic impedance determinedtherefrom by theoretical means. The graphical display of impedanceversus travel time then serves both to delineate layers of the medium 5,if present, such as to identify "normal" sediments in a marine bottom 5,and/or serve as a measure of undissolved gas content, if gassy (perhapspolluted), as previously noted.

Having obtained sampled values of the incident and reflected wavesx_(s), y_(s) respectively, using the above or alternative techniques,deconvolution can be performed using either the following well knowntime-domain algorithm, or alternative means: ##EQU4## where, R_(p) isthe p^(th) sample of a bandlimited equivalent to the reflectionimpulse-response function sampled at intervals T second apart.Integration or the equivalent of integration is performed byalgebraically adding successive values of TR_(p) and the cumulative sumdisplayed (see, as an illustration, the Fourier Integral & ItsApplications, A. Papoulis, McGraw-Hill, 1962, NYC, p. 502, on; withsuitable techniques being of the type disclosed, for example, in TheFourier Transform and Its Applications, R. Bracewell, McGraw-Hill, 1965,NYC, p. 30, on).

Referring to FIGS. 3A and B, a typical display of the integral of thereflection-response function, coined "impedogram," may be produced (FIG.3B) in accordance with the present invention, having correlation withthe actual layers identified within the bottom 5, FIG. 3A. The result isa graphical display, which in the case of unconsolidated sediments,delineates layers and also indentifies the sediment type by use of theindicated quantitative level. For example, the buried "sand" layer inthe sedimentary 5, FIG. 3A, appears as a rise in level 24, FIG. 3B,since the impedance of sand exceeds the impedance of silt. Further down,the gradational blend of silt through silty sand to sand is indicated bya gradual rise in the integral of the reflection impulse-response, ofthe impedogram. Similarly, reflection from "bedrock" or consolidatedsediments, results in a rise to a quantitative level 25, FIG. 3B, whichis too high (greater than say 0.5) for unconsolidated sediments and musttherefore correspond to reflection from consolidated rock, such assandstone, limestone, etc.

In an alternative or equivalent technique, measurements of the abovetype can be made using an impulsive source and one receiver, but makinga pair of measurements at different relative receiver-and-bottomlocations such that, in one measurement, the sediments are closer to thereceiver than in the other. If the waveform emitted by the source isreproducible, then these two waveforms can be used to calculate theincident and reflected waveforms. For example, in a field test of theabove technique, illustrated in FIG. 4, an electrodeless spark acousticimpulsive source 26, and Atlantic Research LC-32 hydrophone 27, weresuspended by their cables over sediments 28, in the Great Harbor atWoods Hole, Massachusetts. Two measurements were made; first, with thereceiver 27 about two feet above the silty bottom 28, and secondly withboth impulse source and receiver lowered about 1.5 feet to positions 29and 30, respectively, so that the receiver was perhaps 0.5 feet abovethe bottom.

By comparing the two waveforms the incident and reflected waveforms wereascertained as follows. The waveform between instants 31 and 32, FIG.4B, is the downgoing or incident waveform; whereas between instants 32and 33, the difference between the two waveforms (shown cross hatched)is the reflected waveform.

This technique is less general than the twin receiver techniquediscussed previously in connection with the embodiment of FIG. 1, but itis simpler and suited to analysis of situations in which the incidentwaveform (not just source-emitted waveform) is reproducible within thetime window of interest.

In field tests, the impulsive source was discharged by an electricalpulse generated by a trigger pulse circuit 31, which triggered a highvoltage energy storage/trigger device 32, and horizontal sweep of acathode-ray oscilloscope 33. Pressure waveforms indicated by hydrophone,27, (30) were low-pass filtered by a Kron-Hite model 3202 electronicfilter, displayed on a Tektronix 535 oscilloscope 33, and photographedwith a Polaroid oscilloscope camera. The waveforms observed weresubstantially similar to those illustrated in FIG. 4. These bandlimitedwaveforms were sampled by reading values at periodic instants directlyfrom the Polaroid photo. The deconvolution, timing and samplingtechniques were as discussed above. By interpreting the reflectionimpulse-response function, the so-called impedogram was obtained of thefirst 1.5 feet of sediment at two different sites in Woods Hole harbor.

The experimentally observed impedogram over a silty bottom is shown inFIG. 5A, and a similar result was obtained over a sandy bottom, as shownin FIG. 5B. In each case, the actual nature of the bottom was determinedby referring to published reports as well as direct visual inspection.In FIGS. 5A and 5B there are bands labeled silt 34, and sand 35, whichwere computed using equation (1) and the published values for "normal"marine sediments. A boundary between silt and sand is also indicated. Itwas found that in each case, the impedogram indicated "correct"quantitative levels corresponding to silt and sand, respectively,thereby demonstrating the reliability of acoustic indentification ofmarine sediments, as discussed above. More precise results and greaterpenetration are obtainable with more sophisticated techniques, aspreviously discussed, also.

The novel results above-discussed, moreover, are all the more startlingin view of the previous experience in the art with acoustic-wavediagnostic devices, which appeared to indicate the necessity forreflection reception in a single, closely-controlled plane. Thedisplaced-plane, colinear, separate receiver technique of the invention,thus departing radically from such prior techniques and teachings, hasenabled a substantial break-through in acoustic identification anddelineation.

It is understood that, in addition to the above preferred technique, theaccuracy of results may be improved by well-accepted techniques known tothose versed in the seismic and related arts, as by operating theapparatus many times at a fixed location, with the waveformsappropriately added so that random, erroneous components will bepreferentially suppressed. Useful sampling, adding and integratingtechniques are described, for example, in the before-mentioned Fouriertexts. The process of device synchronization, described above as amanual task, moreover, may be automated by techniques well known tothose versed in circuit design, or numeric computations can be performedmanually, as by using calculating machines or by more rapid automatedcomputational means, as described, for example, in the PDP-10 ReferenceHandbook, Digital Equipment Corporation, 1969.

With an appropriate modification in the theoretical relationships,moreover, directive sources and/or receivers may also be used.Similarly, results from appropriately spaced, adjacent sites could beadded so as preferentially to suppress events associated with rough,nonplanar interfaces. Successive measurements using progressively sloweror faster sampling rates with correspondingly lower or higher filtercut-off frequencies may also be employed, and the results appropriatelycombined.

The configurational control associated with the rigid device describedin connection with the embodiment of FIG. 1, furthermore, can besacrificed if more complex sampling-rate and sampling-instant criteriaare applied. In this event, less controlled devices may be used,including towed or moveable apparatus. Additionally, as beforeexplained, the principles inherent in the method and apparatus discussedabove can be readily applied to other technical areas to enhanceinformation retrieval and intelligibility of reflected or transmittedwave processes, including radiant electromagnetic wave-energy systems ofany spectral range from visible or invisible light through the radio,microwave and heat spectra. In such event, the source 1 of FIG. 1 may bean electromagnetic transmitter (laser, magnetron, etc.) and thereceivers 2 and 3, appropriate corresponding detectors, as is wellknown. In the acoustic applications, moreover, using higher frequencies,shorter acoustic impulses and faster sampling rates, reflections frommaterials such as so-called laminates can be processed as above, and theresulting impedance vs. time display used for nondestructive diagnosisof, for example, poor laminate bonds resulting from such factors asgaseous inclusions and the like. Similarly, complex impedance profiles,such as might be expected to be associated with biological matter, suchas blood clots, may be profitably examined substantially as above. Inany of these alternative applications, the theoretical relationshipbetween impedance and reflection impulse-response function can beextended to allow for high impedance layers, curvature, directivity orother considerations well known to those versed in acoustic,electromagnetic and seismic signal processing arts.

FIG. 6 illustrates still a further example of the utility of the abovetechniques, described orally by J. P. Jones at the 83rd meeting of theAcoustical Society of America 18-21 April, 1972 at Buffalo, New York. Ina laboratory test using a fragment of human skull bone backed with ablood clot, incident and reflected pulses were deconvolved as discussedabove, the resulting reflection impulse-response function integrated,and apparent impedance with respect to the ambient saline solutiondetermined using the following approximate relationship: ##EQU5##

More generically, for a monotonic increase in impedance, the followingexpression may be used with an iterative technique to correct for higherorder terms as they arrive: ##EQU6## Where C_(n) are coefficients in thesmall value expansion for tanh x, and R_(2n-1) is an 2n-1 numberreflection response.

It is apparent from FIG. 6 that the above-described techniques can be ofgreat utility in the detection, localization, and quantitative measureof human or animal tissue. As a result, the technique is viewed as avaluable tool for applications such as diagnosis of intracranialhematomas (blood clots) and the like.

Similar results have been obtained, as before mentioned, in tests ofmaterials such as bonded laminates of fiber reinforced plastic andrubber.

Additionally, scanning of the detection either mechanically or byelectrical or electronic operation of a multiple array, by well-knowntechniques, may be employed to produce multi-dimensional displays,particularly useful for the diagnosis applications, above mentioned.

Further modifications will also immediately suggest themselves to thoseskilled in these arts, and all such are considered to fall within thespirit and scope of the invention as defined in the appended claims.

What is claimed is:
 1. Apparatus for radiant energy measurement, thatcomprises, means for illuminating a medium with radiant wave energyoutgoing along a predetermined direction, whereby the wave energy isreturned back in substantially the opposite direction from the medium asa result of reflection therefrom, means responsive to the outgoing andreturning wave energy to produce a resulting reflection impulse-responsefunction, means for integrating the said reflection impulse-responsefunction to provide a measure of impedance transitions in the medium,and means for correlating the same with medium properties to identifythe nature of said medium, said function-producing means comprisingmeans for effectively receiving the returning wave energy at samplinginstants of time, said receiving means comprising means for receivingthe returning wave energy at least at two locations in planes spacedalong said predetermined direction and being provided with means foreffecting the receiving within a bandlimiting cut-off frequency, saidilluminating means comprising means for generating wave energy ofsubstantially unipolar impulse form and of pulse duration adjusted notsignificantly to exceed substantially the reciprocal of saidband-limiting cut-off frequency.
 2. Apparatus as claimed in claim 1 andin which said sampling instants are adjusted substantially to theNyquist minimum sampling rate.
 3. Apparatus as claimed in claim 1 and inwhich said sampling instants are selected so that the first nontrivialoutgoing wave sample is maximum.
 4. Apparatus as claimed in claim 1 andin which the waveform of the illuminating wave energy is adjusted toproduce a relatively small (say less than 2) error parameter E_(p) givensubstantially by the expression. ##EQU7## where x_(s) is the s^(th)sample of the illuminating waveform, x_(n+1) is the first nontrivialoutgoing wave sample, and n is an integer.
 5. Apparatus as claimed inclaim 1 and in which said sampling is adjusted substantially inaccordance with the following algorithm criteria: ##EQU8## where x_(s)is the s^(th) sample of the illuminating waveform;Y_(s) is the s^(th)sample of the reflected waveform; P_(s) is the s^(th) sample of the waveenergy from the receiving means at one location; q_(s) is the s^(th)sample of the wave energy from the receiving means at a second location;and m and n are integers.
 6. Apparatus as claimed in claim 1 and inwhich said radiant wave energy is acoustic impulse energy.
 7. Apparatusas claimed in claim 6 and in which the function-producing meanscomprises means for effecting deconvoluting to produce an integral ofsubstantially the form of one of the following equations: ##EQU9## wherez(t) is the relationship between impedance and acoustic travel time t,z_(o) is the specific acoustic impedance of the medium in which thereceiving means is located, C_(n) are coefficients in the small valueexpansion for tanh x, and R_(2n-1) is a 2n-1 number reflection response.8. Apparatus adapted for seismic applications and as claimed in claim 6and in which said medium is a geological medium.
 9. Impedance transitionradiant-energy measuring apparatus adapted for seismic applicationshaving, in combination, a source of radiant acoustic wave energyprovided with means for positioning the source above a geological mediumsurface and means for directing the energy outgoing along apredetermined direction to illuminate said medium with such energy, saidsource comprising means for generating substantially unipolartime-asymmetric impulses of such wave energy; radiant acoustic waveenergy receiving means having means for positioning the same above saidmedium surface and between said source and said medium in the path ofsuch illumination to receive the reflected energy returning in theopposite direction from said medium at least at two locationsdifferently spaced from said medium; means connected with said receivingmeans for deconvoluting the outgoing and returning wave energy toproduce a resulting reflection impulse-response function; meansresponsive to the deconvoluting means for integrating the saidreflection impulse-response function to provide a measure of impedancetransitions in the medium; and display means connected to indicate theintegrated function and enable correlation of the same with mediumproperties to identify the nature of said medium.
 10. Impedancetransition radiant-energy measuring apparatus as claimed in claim 9 andin which said receiving and deconvoluting means are responsive to andcontrolled by sampling means adjusted substantially to at least one ofthe Nyquist minimum sampling rate, and sampling instants such that thefirst nontrivial outgoing wave sample is substantially maximum. 11.Impedance transition radiant-energy measuring apparatus as claimed inclaim 9 and in which at least one of the said source and sampling meansis provided with means for adjustment to produce a relatively smallerror parameter Ep given substantially by the expression ##EQU10## wherex_(s) is the s^(th) sample of the illuminating waveform, x_(n+1) is thefirst non trivial outgoing wave sample, and n is an integer. 12.Impedance transition radiant-energy measuring apparatus as claimed inclaim 9 and in which said receiving means are provided with multiplestage filter means tuned to provide a predetermined bandlimiting cut-offfrequency, and in which means is provided for adjusting the source pulseduration not significantly to exceed substantially the reciprocal of thesaid bandlimiting cut-off frequency.
 13. Apparatus as claimed in claim 1and in which the function-producing means comprises means for effectingdeconvoluting with substantially the algorithm criteria of the followingequation: ##EQU11## where, R_(P) is the p^(th) sample of a bandlimitedequivalent to the reflection impulse-response function sampled atintervals T second apart,where y_(p) is the p^(th) sample of thereflected waveform;where x_(s) is the s^(th) sample of the illuminatingwaveform;where x_(n+1) is the first nontrivial outgoing wave sample; andn is an integer.
 14. Apparatus as claimed in claim 1 and in which saidradiant energy is electromagnetic.
 15. A method of radiant energymeasurement, that comprises, illuminating a medium with radiant waveenergy outgoing along a predetermined direction, returning the waveenergy back in substantially the opposite direction from the medium as aresult of reflection therefrom, responding to the outgoing and returningwave energy to produce a resulting reflection impulse-response function,integrating the said reflection impulse-response function to provide ameasure of impedance transitions in the medium, and correlating the samewith medium properties to identify the nature of said medium, saidresponding comprising effectively receiving the returning wave energy atsampling instants of time at least at two locations in planes spacedalong said predetermined direction and deconvoluting the outgoing andreturning wave energy in the time domain, said receiving being effectedwithin a band limiting cut-off frequency, and said illuminating waveenergy being of substantially unipolar impulse form and of pulseduration adjusted not significantly to exceed substantially thereciprocal of said band limiting cut-off frequency.
 16. A method asclaimed in claim 15, and in which said sampling instants are adjustedsubstantially to the Nyquist minimum sampling rate.
 17. A method asclaimed in claim 15, and in which said sampling instants are selected sothat the first nontrivial outgoing wave sample is maximum.